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Abstract

Rank transformations are frequently employed in numerical experiments involving a computational model, especially in the context of sensitivity and uncertainty analyses. Response surface replacement and parameter screening are tasks which may benefit from a rank transformation. Ranks can cope with nonlinear (albeit monotonic) input-output distributions, allowing the use of linear regression techniques. Rank transformed statistics are more robust, and provide a useful solution in the presence of long tailed input and output distributions. In the study reported here an heuristic approach is taken, to explore, by way of practical examples, the effect of a rank transformation on the outcome of a sensitivity analysis. An attempt is made to identify trends, and to correlate these effects to a model taxonomy. Results show that the main effect of the rank transformation is to increase the relative weight of the first order terms (the 'main effects'), at the expense of the 'interactions' and 'higher order interactions'. It is suggested that models can be ranked, with respect to the complexity of their input-output relationship, by mean of an 'Association' index I(y). I(y) may complement the usual model coefficient of determination as a measure of model complexity for the purpose of uncertainty and sensitivity analysis.

Additional information

Authors: SALTELLI A, JRC Ispra (IT);SOBOL I M, National Centre for Mathematical Modelling of the Russian Academy of Science, Moscow (SU)
Bibliographic Reference: Article: Reliability Engineering and System Safety, Vol. 50 (1995) No. 3, pp. 225-239
Availability: Available from Dr A Saltelli, Atmospheric Chemistry Unit, Joint Research Centre, 21020 Ispra (IT)
Record Number: 199610302 / Last updated on: 1996-03-29
Category: PUBLICATION
Original language: en
Available languages: en